It is well known that, if one bit message is encoded in one of binary standard coherent states (S-CS), a quantum measurement achieving the Helstrom bound[1]} is described by a projective measurement composed of orthogonal Schrödinger cat states[2]}, [3]}. However, the unitary operator for controlling the Schrödinger cat states is not Gaussian[3]}, which makes it difficult to implement the projective measurement via linear optics[5]}. Thus, the previous unconventional measurements took the experimental form including displacement operation and detection of photon numbers[6]}, [7]} instead of implementing optimal projective measurements.
